In recent years, great progress has been made in the technical aspects of automatic speaker verification (ASV). However, the promotion of ASV technology is still a very challenging issue, because most technologies are still very sensitive to new, unknown and spoofing conditions. Most previous studies focused on extracting target speaker information from natural speech. This paper aims to design a new ASV corpus with multi-speaking styles and investigate the ASV robustness to these different speaking styles. We first release this corpus in the Zenodo website for public research, in which each speaker has several text-dependent and text-independent singing, humming and normal reading speech utterances. Then, we investigate the speaker discrimination of each speaking style in the feature space. Furthermore, the intra and inter-speaker variabilities in each different speaking style and cross-speaking styles are investigated in both text-dependent and text-independent ASV tasks. Conventional Gaussian Mixture Model (GMM), and the state-of-the-art x-vector are used to build ASV systems. Experimental results show that the voiceprint information in humming and singing speech are more distinguishable than that in normal reading speech for conventional ASV systems. Furthermore, we find that combing the three speaking styles can significantly improve the x-vector based ASV system, even when only limited gains are obtained by conventional GMM-based systems.